Question

Which of the following equations have no solutions?

Choose all answers that apply:
Choose all answers that apply:

(Choice A)
A
-60x+32=-60x+60−60x+32=−60x+60minus, 60, x, plus, 32, equals, minus, 60, x, plus, 60

(Choice B)
B
-60x+32=32x-60−60x+32=32x−60minus, 60, x, plus, 32, equals, 32, x, minus, 60

(Choice C)
C
-60x+32=-60x-32−60x+32=−60x−32minus, 60, x, plus, 32, equals, minus, 60, x, minus, 32

(Choice D)
D
-60x+32=32x+60−60x+32=32x+60

Answer 1

The equations in choice A (-60x + 32 = -60x + 60) and choice C (-60x + 32 = -60x - 32) have no solutions because they lead to contradictory statements when we attempt to solve for x.

Step-by-step explanation:

To determine which of the following equations have no solutions, we need to analyze each equation to see if it's possible to find a value of x that would satisfy the equation.

(Choice A) -60x + 32 = -60x + 60: Here, if we try to isolate x on one side, we end up with an impossibility because subtracting -60x from both sides gives 32 = 60, which is not true. Therefore, this equation has no solutions.

(Choice B) -60x + 32 = 32x - 60: This is a standard linear equation that can potentially be solved for x, and thus can have a solution.

(Choice C) -60x + 32 = -60x - 32: Similar to choice A, subtracting -60x from both sides yields 32 = -32, which is a contradiction. Hence, this equation also has no solutions.

(Choice D) -60x + 32 = 32x + 60: This equation is solvable as it involves a linear equation with variable x on both sides, suggesting that it can have a solution.

Based on the analysis, the equations in choice A and choice C have no solutions, as they lead to contradictory statements when we attempt to solve for x.